1.

Title : Three lectures on "Borcherds products, Green functions, and their CM values"

Speaker : Prof. Jan Bruinier (TU Darmstadt)

Lecture 1 : "Borcherds products"

Abstract : We give an introduction to the theory of Borcherds products and the regularized theta correspondence.

Lecture 2 : "Automorphic Green functions and the Gross-Zagier formula"

Abstract : Theta lifts of weak Maass forms give rise to automorphic Green functions.

We explain how these can be used to compute height pairings of Heegner divisors and to prove Gross-Zagier type formulas.

Lecture 3 : "CM values of higher Green functions"

Abstract : So called higher Green functions are obtained by specializing automorphic Green functions to positive integral values of the spectral parameter.

We discuss some new results regarding the algebraicity properties of their CM values,

as well as higher variants of the Gross-Kohnen-Zagier theorem.

2.

Title : Three lectures on "Modular forms of half-integral weight: old and new results".

Speaker : Prof. Winfried Kohnen (Univ. of Heidelberg)

Lecture 1 : Basic concepts of the theory

Abstract : "We will introduce the basic definitions and features of the theory, including the Shimura lift and Waldspurger's theorem"

Lecture 2 : Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight

Abstract : We shall prove a non-vanishing results for the product of two Fourier coefficients of cusp forms of half-integral weight in weight aspect"

Lecture 3 : The Ramanujan-Petersson conjecture

Abstract : "We will discuss various aspects of the Ramanujan-Petersson conjecture in the case of half-integral weight"

<Schedule>

Date	Time and Title
June 2 (Sun)	11:00-12:15	Lecture 1 (Bruinier)
	14:00-15:15	Lecture 1 (Kohnen)
	15:45-17:00	Lecture 2 (Bruinier)
June 3 (Mon)	11:00-12:15	Lecture 2 (Kohnen)
	14:00-15:15	Lecture 3 (Bruinier)
	15:45-17:00	Lecture 3 (Kohnen)